/*
 * @lc app=leetcode.cn id=37 lang=cpp
 *
 * [37] 解数独
 *
 * https://leetcode-cn.com/problems/sudoku-solver/description/
 *
 * algorithms
 * Hard (67.39%)
 * Likes:    1246
 * Dislikes: 0
 * Total Accepted:    141K
 * Total Submissions: 209.1K
 * Testcase Example:  '[["5","3",".",".","7",".",".",".","."],["6",".",".","1","9","5",".",".","."],[".","9","8",".",".",".",".","6","."],["8",".",".",".","6",".",".",".","3"],["4",".",".","8",".","3",".",".","1"],["7",".",".",".","2",".",".",".","6"],[".","6",".",".",".",".","2","8","."],[".",".",".","4","1","9",".",".","5"],[".",".",".",".","8",".",".","7","9"]]'
 *
 * 编写一个程序，通过填充空格来解决数独问题。
 * 
 * 数独的解法需 遵循如下规则：
 * 
 * 
 * 数字 1-9 在每一行只能出现一次。
 * 数字 1-9 在每一列只能出现一次。
 * 数字 1-9 在每一个以粗实线分隔的 3x3 宫内只能出现一次。（请参考示例图）
 * 
 * 
 * 数独部分空格内已填入了数字，空白格用 '.' 表示。
 * 
 * 
 * 
 * 
 * 
 * 
 * 示例 1：
 * 
 * 
 * 输入：board =
 * [["5","3",".",".","7",".",".",".","."],["6",".",".","1","9","5",".",".","."],[".","9","8",".",".",".",".","6","."],["8",".",".",".","6",".",".",".","3"],["4",".",".","8",".","3",".",".","1"],["7",".",".",".","2",".",".",".","6"],[".","6",".",".",".",".","2","8","."],[".",".",".","4","1","9",".",".","5"],[".",".",".",".","8",".",".","7","9"]]
 * 
 * 输出：[["5","3","4","6","7","8","9","1","2"],["6","7","2","1","9","5","3","4","8"],["1","9","8","3","4","2","5","6","7"],["8","5","9","7","6","1","4","2","3"],["4","2","6","8","5","3","7","9","1"],["7","1","3","9","2","4","8","5","6"],["9","6","1","5","3","7","2","8","4"],["2","8","7","4","1","9","6","3","5"],["3","4","5","2","8","6","1","7","9"]]
 * 解释：输入的数独如上图所示，唯一有效的解决方案如下所示：
 * 
 * 
 * 
 * 
 * 
 * 
 * 提示：
 * 
 * 
 * board.length == 9
 * board[i].length == 9
 * board[i][j] 是一位数字或者 '.'
 * 题目数据 保证 输入数独仅有一个解
 * 
 * 
 * 
 * 
 * 
 */

// @lc code=start
class Solution {
    // bool backtracking(vector<vector<char>>& board) {
    //     for(int i = 0; i < 9; i++) {
    //         for(int j = 0; j < 9; j++) {
    //             if(board[i][j] != '.') continue;
    //             for(char val = '1'; val <= '9'; val++) {
    //                 if(isValid(i, j, board, val)) {
    //                     board[i][j] = val;
    //                     if(backtracking(board)) return true;
    //                     board[i][j] = '.';
    //                 }
    //             }
    //             return false;
    //         }
    //     }
    //     return true;
    // }
    // bool isValid(int row, int col, const vector<vector<char>>& board, char val) {
    //     //判断行
    //     for(int i = 0; i < 9; i++) {
    //         if (board[row][i] == val) return false; 
    //     }
    //     //判断列
    //     for(int i = 0; i < 9; i++) {
    //         if(board[i][col] == val) return false;
    //     }
    //     //判断九宫格
    //     int startRow = (row / 3) * 3;
    //     int startCol = (col / 3) * 3;
    //     for(int i = startRow; i < startRow + 3; i++) {
    //         for(int j = startCol; j < startCol + 3; j++) {
    //             if(board[i][j] == val) return false;
    //         }
    //     }
    //     return true;
    // }

//复盘
private:
    bool backtracking(vector<vector<char>>& board) {
        for(int row = 0; row < 9; row++) {
            for(int col = 0; col < 9; col++) {
                if(board[row][col] != '.') continue;
                for(char val = '1'; val <= '9'; val++) {
                    if(isValid(row, col, val, board)) {
                        board[row][col] = val;
                        if(backtracking(board)) return true;
                        board[row][col] = '.';
                    }
                }
                return false;
            }
        }
        return true;
    }

    bool isValid(int row, int col, char val, vector<vector<char>> board) {
        for(int i = 0; i < 9; i++) {
            if(board[row][i] == val) return false;
        }

        for(int i = 0; i < 9; i++) {
            if(board[i][col] == val) return false;
        }

        int startRow = (row / 3) * 3;
        int startCol = (col / 3) * 3;
        for(int i = startRow; i < startRow + 3; i++) {
            for(int j = startCol; j < startCol + 3; j++) {
                if(board[i][j] == val) return false;
            }
        }
        return true;
    }
public:
    void solveSudoku(vector<vector<char>>& board) {
        backtracking(board);
        return;
    }
};
// @lc code=end

